Signed Formulae as a New Update Process

Signed Formulae as a New Update Process

Fernando Zacarías Flores (Benemérita Universidad Autónoma de Puebla, Mexico), Dionicio Zacarías Flores (Benemérita Universidad Autónoma de Puebla, Mexico), Rosalba Cuapa Canto (Benemérita Universidad Autónoma de Puebla, Mexico) and Luis Miguel Guzmán Muñoz (Benemérita Universidad Autónoma de Puebla, Mexico)
Copyright: © 2009 |Pages: 7
DOI: 10.4018/978-1-59904-849-9.ch209
OnDemand PDF Download:
$37.50

Abstract

The agent paradigm has recently increased its influence in the research and development of computational logicbased systems. A clear and correct specification is made through Logic Programming (LP) and Non-nomotonic Reasoning that have been brought (back) to the spotlight. Also, the recent significant improvements in the efficiency of LP implementations for Non-monotonic Reasoning (De Schreye, Hermenegildo & Pereira, 1999) have helped to this resurgence. However, the agents need update constantly their knowledge base and, particularly the intentional base (rules) such that our agent has the ability to reacting to changes in dynamic environments is of crucial importance within the context of software agents. Such feature should correspond to a deliberative rational behavior wanted for our agents. The quality of the service that an agent offers is based on the form in which an agent combines rationality and reactivity. A reactive agent can offer well evaluated recommendations but, this response is based on outdated information, while a rational behavior may generate recommendations based on the most recently acquired information. So, we are interested in developing environment-aware agents. For this reason, is very important to have an update process for agents, i.e., that it allows us to design agents with its rational component. Over recent years, several semantics for logic program updates have been proposed (Brewka, Dix, & Knonolige 1997) (De Schreye, Hermenegildo, & Pereira, 1999) (Katsumo & Mendelzon, 1991). All these semantic ones coincide in considering the AGM proposal as the standard model in the update theory, for their wealth in properties. The AGM approach, introduced in (Alchourron, Gardenfors & Makinson, 1985) is the dominating paradigm in the area, but in the context of monotonic logic. All these proposals analyze and reinterpret the AGM postulates under the Answer Set Programming (ASP) such as (Eiter, Fink, Sabattini & Thompits, 2000). However, the majority of the adapted AGM and update postulates are violated by update programs, as shown in (De Schreye, Hermenegildo, & Pereira, 1999). For this reason, we have been working in finding properties that our update operator satisfies (Osorio & Zacarías, 2003) (Zacarías & Osorio, 2005) (Arrazola & Zacarias, 2005). Our purpose is to build a semantics based on structural properties. This is our main objective in the update theory. In (De Schreye, Hermenegildo, & Pereira, 1999) (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005) the authors present a set of properties that the update operator satisfies. In this paper we continue with this same research line presenting a novel proposal with the aim to enrich the update theory that we have begun in (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005). This novel proposal contributes with two benefits. First, we conserve many of the properties presented in previous works (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005), such as: Weak Irrelevance of Syntax (WIS). This property is similar to one postulate proposed by AGM, but in this case for nonmonotonic logic and under Answer Set Programming (ASP) introduced and defined by (Gelfond & Lifschitz, 1988).
Chapter Preview
Top

Introduction

The agent paradigm has recently increased its influence in the research and development of computational logic-based systems. A clear and correct specification is made through Logic Programming (LP) and Non-nomotonic Reasoning that have been brought (back) to the spot-light. Also, the recent significant improvements in the efficiency of LP implementations for Non-monotonic Reasoning (De Schreye, Hermenegildo & Pereira, 1999) have helped to this resurgence. However, the agents need update constantly their knowledge base and, particularly the intentional base (rules) such that our agent has the ability to reacting to changes in dynamic environments is of crucial importance within the context of software agents. Such feature should correspond to a deliberative rational behavior wanted for our agents.

The quality of the service that an agent offers is based on the form in which an agent combines rationality and reactivity. A reactive agent can offer well evaluated recommendations but, this response is based on outdated information, while a rational behavior may generate recommendations based on the most recently acquired information. So, we are interested in developing environment-aware agents. For this reason, is very important to have an update process for agents, i.e., that it allows us to design agents with its rational component.

Over recent years, several semantics for logic program updates have been proposed (Brewka, Dix, & Knonolige 1997) (De Schreye, Hermenegildo, & Pereira, 1999) (Katsumo & Mendelzon, 1991). All these semantic ones coincide in considering the AGM proposal as the standard model in the update theory, for their wealth in properties. The AGM approach, introduced in (Alchourron, Gardenfors & Makinson, 1985) is the dominating paradigm in the area, but in the context of monotonic logic. All these proposals analyze and reinterpret the AGM postulates under the Answer Set Programming (ASP) such as (Eiter, Fink, Sabattini & Thompits, 2000). However, the majority of the adapted AGM and update postulates are violated by update programs, as shown in (De Schreye, Hermenegildo, & Pereira, 1999). For this reason, we have been working in finding properties that our update operator satisfies (Osorio & Zacarías, 2003) (Zacarías & Osorio, 2005) (Arrazola & Zacarias, 2005). Our purpose is to build a semantics based on structural properties. This is our main objective in the update theory. In (De Schreye, Hermenegildo, & Pereira, 1999) (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005) the authors present a set of properties that the update operator satisfies. In this paper we continue with this same research line presenting a novel proposal with the aim to enrich the update theory that we have begun in (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005). This novel proposal contributes with two benefits. First, we conserve many of the properties presented in previous works (Osorio & Zacarias, 2003) (Zacarías, Osorio & Arrazola, 2005) (Zacarias, 2005), such as: Weak Irrelevance of Syntax (WIS). This property is similar to one postulate proposed by AGM, but in this case for nonmonotonic logic and under Answer Set Programming (ASP) introduced and defined by (Gelfond & Lifschitz, 1988).

Key Terms in this Chapter

Principle of Irrelevance of Syntax: The meaning of the knowledge that results from an update must be independent of the syntax of the original knowledge, as well as independent of the syntax of the update itself.

Intelligent Agent: An intelligent agent is a component of software (or hardware) that it perceives and it acts autonomously in an open and dynamic environment, learning and cooperating with other agents (the same user) to offer a benefit to their user.

Equivalence: Two programs are equivalent if they have exactly the same answer sets.

Strong Equivalence: (Lifschitz, Pearce & Valverde, 2001). We say that P1 and P2 are strongly equivalent if for every program P, P1 ? P and P2 ? P have the same answer sets.

Weak Irrelevance of Syntax: T1 = T2 implies Bel(K ? T1) = Bel(K ? T2), where K, T1 and T2 are any theories, Bel(T) defines the set of answer sets of T, ? is the update operator, and understanding that equivalence means that both programs (T1 and T2) have the same answer sets.

Update: Let P be the program representing the current knowledge base, if it is updated by another program U, then PU is a program updated of P if only if the models of PU are the result of updating each of the models of P according to a given semantics S; to each of these models apply the update request U to obtain a new set of models M; PU is any logic program whose models are exactly M.

Beliefs: An agent whose knowledge base is the theory T believes F if and only if F belongs to every intuitionistically complete and consistent extension of T by adding only negated literals.

Complete Chapter List

Search this Book:
Reset